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Lauren runs a bike shop and sell bikes for $165 each. The daily cost function is C(q) = 400q+400/q+4, where the costs are in
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Answer #1

C (q) = 400q + (400 / q) + 4

Price per bike = $165

Total Revenue = p * q = $165q

a) Daily profit function = Total Revenue - Total Cost = 165q - 400q - (400 / q) - 4 = - 235q - (400 / q) - 4

b) Break - even quantity occurs when Total Revenue = Total Cost

165q = 400q + (400 / q) + 4

235q + (400 / q) + 4 = 0

235q^2 + 4q + 400 = 0

This can never be possible as coefficients of all terms is positive whose sum cannit be zero, it would always be greater than 0.

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